I'm not sure how to apply the Ito's calculus in the determination of an asset price at a given time T=t based on the Ito's lemma and a geometric brownian motion the asset price follows:
Assume: $S(t,X(t)) = S_0e^{ut + \sigma X(t)}$ given a known $S_0 = 100$, $u = .08$ and $\sigma^2 = .05$ and where $X(t)$ is a geometric brownian motion and $u$ and $\sigma$ are monthly parameters.
I can apply Ito's Lemma to compute $dS$
$dS/S = (u + \sigma^2)dt + \sigma dBt$
However I'm unclear how to compute S(t=3) given the monthly parameters. How do I take into account the brownian motion X(t) to arrive at a value given $S_0$ = 100 at S(3)?